Leonard E Parker Center for Gravitation, Cosmology and Astrophysics

The broadband LIGO-Virgo experiment is designed to detect gravitational waves (GWs) over a frequency range spanning from tens to thousands of Hz, using a network of interferometers in Hanford, WA, Livingston Parish, LA and Cascina, Italy. The interferometers each have arms up to 4 km in length on a side, and have been down for upgrades since October 2010 that are designed to make these instruments more sensitive to GW transients in the local universe. Scheduled to come back online in autumn 2015, the interferometers will continue to improve sensitivity steadily over the course of the next three years, until finally reaching design sensitivity in 2018. This is the era of Advanced LIGO and Advanced Virgo, and it promises to provide a rich new understanding of a host of open problems in astrophysics.

Among these open problems is the radiative loss of energy between two compact bodies (such as a neutron star and a black hole), leading to a decaying orbit and ultimately to a merger of the two bodies. The energy loss typically occurs over hundreds of millions of years as the orbital energy is slowly radiated in the form of gravitational waves, and this effect has been observed indirectly in the Hulse-Taylor binary pulsar PSR B1913+16. GWs from the final few minutes of the inspiral are emitted with frequencies in the ~10-5000 Hz range over which LIGO and Virgo are sensitive. But there are also scenarios where this compact binary coalescence acts as an engine powering other known phenomena in high-energy astrophysics such as short gamma-ray bursts (GRBs), ghostly optical afterglows and so-called kilonovae (which should be visible in the near infrared). Therefore, a crucially important science driver in the advanced detector era is to coordinate astronomical follow-up of candidate GW signals, in order to learn as much as possible about the physics of the merger process. But more than that, these events are fleeting: GRBs occur within seconds of the merger and last for only fractions of a second, while optical afterglows occur within minutes of the merger and remain detectably bright only for ~1 day. If our efforts are to be successful, then it is also crucial to act fast, communicating information to astronomy colleagues in real time.

Easily the most relevant information for astronomers is the transient outburst's location on the sky, as this makes it possible to save precious time by already knowing where to point a telescope. There has been a directed effort by data analysts in LIGO and Virgo to make "sky maps" available in low latency (within a few minutes of the GW candidate) using the BAYESTAR (BAYESian optimal Search for Transients with Autonomous and Robotic telescopes) position reconstruction code. This algorithm makes use of timing information across the detector network to triangulate the signal, then further narrows down sky location using amplitude and phase sensitivity of the detectors, all within the framework of Bayes' theorem. BAYESTAR is able to do this so rapidly because right ascension and declination are the only two parameters it is designed to provide posteriors for. Other algorithms use stochastic sampling to measure the full range of parameters -- including masses, spins, the distance to source, and the inclination, phase and polarization angles -- and can improve significantly on the sky location measurement if the signal happens to be very weak in one detector. However, this improvement comes at significant computational cost, and in most cases means the updated sky location posterior takes several hours or even days to compute compared to BAYESTAR's few minutes (see Figs. 1 and 2).

To describe some realistic observing prospects for the advanced detector era, we simulated a population of binary neutron star (BNS) mergers and injected them into Gaussian noise based on the commissioning schedule of the LIGO and Virgo instruments in two epochs: first, a 2015-era scenario with two detectors (H1 in Hanford, WA and L1 in Livingston, LA) at comparable sensitivities; second, a 2016-era scenario with H1 and L1 at improved sensitivity and the Virgo detector (V1) introduced at lower sensitivity compared to the other two. We reconstruct sky positions with BAYESTAR and two stochastic sampling codes called LALInference_Nest and LALInference_MCMC, comparing the sky maps they provide with the true location of the injected GW signals. Briefly, in 2015, we find that BAYESTAR and the LALInference codes each produce sky maps whose 50% confidence contours enclose ~100 square degrees on average, and there is very little improvement of one over the other (see Fig. 3). This comes down to the fact that the detectors have nearly identical sensitivity. Furthermore, because there are only two detectors most 2015 sky maps tend to have broad ring-like shapes with one or two "islands" of probability (one usually in the northern and the other in the southern hemisphere). In 2016, where H1 and L1 become more sensitive and V1 is introduced, more complicated sky map morphologies arise while the median 50% contour size is a factor of ~5-6 smaller for LALInference sky maps than BAYESTAR ones because distant signals are much weaker in V1. However, the upshot is that LALInference can take a day or more to provide improved localization, while BAYESTAR has the information to hand within a few minutes of news arriving of an event.

Some likely observing strategies begin to emerge as a result of this study. For example, since most high-cadence, wide-field telescopic surveys are already accustomed to following up GRB triggers, much of the infrastructure for GW follow-up already exists in the form of the Gamma-ray Coordinates Network (GCN) which can be used by LIGO and Virgo to broadcast sky maps and other information to the astronomical community. However, most GRB sky maps (provided by the Swift and Fermi gamma-ray satellites) are shaped like Gaussian blobs, while we have shown LIGO-Virgo sky maps will have much more complicated morphological structure. This will require careful thinking to arrive at an optimal tiling strategy for optical telescopes. To that end, a public data release accompanying this study contains a large catalogue of simulated sky maps that typify what is expected when LIGO and Virgo actually come online. We encourage members of the larger scientific community to use these data as they put together plans for electromagnetic follow-up, and join in the conversation of how best to coordinate multimessenger astronomy efforts going forward.

Fig. 2: The timescale over which electromagnetic signatures accompanying compact mergers remain visible (top row) compared to a realistic timeline of when data products are made available by LIGO and Virgo to the astronomical community. Credit: L.P. Singer.

Fig. 3: Cumulative histogram of the minimum searched sky area in the simulated 2015 (left) and 2016 (right) detection scenarios. The searched area statistic is defined as the minimum area searched by a telescope, starting at the absolute maximum of the sky location posterior, before finding the true location of the source. Here the red curves correspond to BAYESTAR sky maps while the blue curves correspond to LALInference_MCMC/LALInference_Nest sky maps. Note that in 2015, where the two detectors are of a comparable sensitivity, there is only modest improvement in localization ability between BAYESTAR and the stochastic sampling codes; while in 2016, where Virgo is introduced at far lower sensitivity, the stochastic codes offer almost an order of magnitude improvement in searched sky area.